SOLUTION: Write out, in paragraph form, a plan for completing the following proof. For example, will you prove triangles congruent? How? By what theorem? Given: AR = AQ RT = QS Prov

Algebra ->  Geometry-proofs -> SOLUTION: Write out, in paragraph form, a plan for completing the following proof. For example, will you prove triangles congruent? How? By what theorem? Given: AR = AQ RT = QS Prov      Log On


   

Question 1043803: Write out, in paragraph form, a plan for completing the following proof.
For example, will you prove triangles congruent? How? By what theorem?
Given:
AR = AQ
RT = QS
Prove:
RAT = QAS
Link to triangle...
https://rlcs.ignitiaschools.com/media/g_geo_ccss_2016/4/page47a.gif
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
RT-ST=QS-ST, because subtracting the same quantity from two lines that have been stated to be equal.
Therefore RS=TQ
Angle R=Angle Q, because it is an isosceles triangle
Triangle AR
S is congruent to ATQ.
AT=AS
Because TAS is isosceles, angles 5 and 6 are equal.
Therefore, angles 4 and 7 are equal, because they are supplementary angles of the same angle.
And angles 1 and 3 are equal, because the other two angles in the triangle are equal.


The triangles RAT and QAS are congruent with SAS.